Havana is abuzz at the sheer weight of the president of the United States arriving in Cuba. In the hours before President Obama’s arrival, astonished Cubans told tales of planeloads of black limousines and massive Suburbans, of heavily armed security personnel, of sunglass-sporting secret service officers arriving at the airport and making their way through the city.

Cubans have anticipated the arrival of the Obama family with considerable joyfulness, but the festive mood is colored by a certain reticence, a deep-seated fear of, once again, being overwhelmed by the Colossus from the North.

The government has bargained hard with Obama’s advance team to hem him in, to limit his direct contact with the Cuban people. There will be no large outdoor speech—rather on Tuesday morning Obama will address a hand-picked audience in the newly renovated Grand Theatre with its limited seating capacity—although the Cuban government agreed to live television coverage. The U.S. president will also meet with local entrepreneurs, but in a constricted venue, and ditto for his meeting with independent civil society and political dissidents.

On Tuesday afternoon the president will be the guest of honor at an exhibition game between the visiting Tampa Bay Rays (their chance selection was by lottery) and the Cuban national team. The White House has hinted that he will throw out the first ball, but this could not be confirmed. On a prior occasion, Jimmy Carter did indeed throw out the first ball, but that was during a visit long after his presidency.

Putting the lanky, athletic Obama on the mound would run a certain risk for the Cubans. Suppose the excited crowd begins to cheer, “Obama, Obama…” Even more dangerous, imagine if the exuberant Cubans follow with, “USA, USA, USA…”

Back home, critics of the Obama administration say he’s made too many concessions to the Cuban government without reciprocity. Cuba is no closer to a liberal democracy, they argue, than it was on December 17, 2014, when Barack Obama and Raúl Castro announced their decision to normalize diplomatic relations. But these skeptics miss this vital point: By befriending the president of the United States, the president of Cuba and first secretary of the Cuban Communist Party (PCC) has exploded his regime’s long-standing national security paradigm organized around the imminent danger posed by a hostile empire. The rationale for the state-of-siege mentality, the explanation for the poor economic performance, no longer resonates. The ruling political bureau of the PCC stands exposed before the Cuban people.

Hence, the government is working hard to persuade the people that it has not forsaken its nationalist credentials: the PCC’s daily newspaper, Gramna, ran a fierce editorial warning for Obama not to try to step on their little island, not to intervene in its internal affairs; rather, he must arrive as a classic Greek suitor bearing gifts. But no Trojan horses, the Cubans are too wary to be fooled so easily.

Venezuelan President Nicolás Maduro, passing through Havana this week, pointedly remarked: “The hearts of the Cuban and Venezuelan people are warm and true. Not like others who come with smiles but hide a clenched fist.”

In truth, most Cubans very much want the trip to succeed. They want more tourists, more remittances from Cuban-Americans living in Florida and New Jersey. They would welcome more trade, more access to famous U.S. consumer brands. Many would even welcome U.S. investment—with the promise of good jobs and better wages. All would love to be able to travel freely between their island and the outside world, especially to the nearby United States. In short, they yearn for normality.

And savvy Cubans sense the link between the more relaxed diplomatic atmosphere and the gradual opening of political space so evident on the island. While not yet living in a fully open society, Cubans are now more willing to express their views openly, to foreigners and among themselves. Some are even forming proto-civil society groupings, to advance gender equality, environmental stewardship, religious freedom, and human rights.

Bathing in these new liberties, Cubans worry that something, anything, could go wrong during the visit. In such a highly scrutinized setting, one misstep, one awkward phrase, one misinterpretation of Cuban history, would give ammunition to hardliners to set the clock back and to restore the old national security paradigm.

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Raúl Castro has pinned his own legacy too closely to the young U.S. president to allow any stumbles during this historic visit, to stand idly by while the visit was twisted by his internal opponents. And Raúl and his confidants retain control over the mass media in Cuba, and the PCC will loyally pass along the party line, as set by the political bureau and echoed all along the chain of command, down to the district and village level.

So the visit will be declared a success. Most likely, it will truly be a marvelous moment, because Obama is just the right person to stretch out the U.S. hand to the long-aggrieved Cuban people. The very traits for which Obama is so often criticized at home will serve him well in Cuba: his humility, his respectfulness, his sense of irony—these are just what Cubans have been harking for from the United States for so many decades.

The Cubans will also love Michelle Obama and the two teenage Obama daughters, especially if Sasha and Malia are freed to wander forth and meet their contemporaries at one of Havana’s clubs where young people gather—the Cuban media and public will bask in the respect being paid to Cuban music and dance, to “Cubanismo.”

Obama and Castro share some goals, and conflict on others. Both wish for a peaceful transition to a more prosperous Cuba, more open to the world and to global commerce. But they differ on the endgame: Obama would like to see a more liberal, pluralistic polity, while Castro presumably wants to see his Communist Party retain its grip on power. But that chess match will be waged later, by their successors.

For Barack Obama and Raúl Castro, today their interests are convergent. Hence, we can predict that, most likely, the visit will be a great success, a historic legacy for which both statesmen will be justly proud.